Four sub-Jovian-mass planets detected by high-cadence microlensing surveys

During the 2010s, microlensing entered an era of high-cadence surveys with the instrumental upgrade of previously established experiments and the participation of a new experiment. The new era started when the Microlensing Observations in Astrophysics survey (MOA: Bond et al., 2001), which had previously carried out a lensing survey using a 0.61 m telescope and a camera with a 1.3 deg² field of view (FOV) during the early phase, launched its second phase experiment with the employment of a 1.8 m telescope equipped with a wide-field camera yielding a 2.2 deg² FOV. Since its first operation in 1992, the Optical Gravitational Lensing Experiment (OGLE) has been upgraded multiple times, and it is in its fourth phase (OGLE-IV: Udalski et al., 2015) with the employment of a 1.3 m telescope and a camera with a 1.4 deg² FOV. The Korea Microlensing Telescope Network (KMTNet: Kim et al., 2016), which was launched in 2016, is being carried out with the use of three globally distributed 1.6 m telescopes, each of which is mounted with a wide-field detector providing a 4 deg² FOV. With the use of wide-field cameras mounted on multiple telescopes, the current lensing surveys can monitor lensing events with a dramatically enhanced observational cadence.

The greatly increased observational cadence of the lensing surveys has brought out important changes not only in the observational strategy but also in the outcome of planetary microlensing searches. First, being able to resolve short-lasting planetary signals from survey observations, the high-cadence surveys can function without the survey+followup experiment mode, in which low-cadence surveys mainly detect and alert lensing events and followup groups densely observe the alerted events. Second, the number of microlensing planets has substantially increased with the operation of the high-cadence surveys. Among the total 135 microlensing planets with measured mass ratios²²2The sample includes 119 planets listed in the NASA Exoplanet Archive (https://exoplanetarchive.ipac.caltech.edu/index.html) plus 16 planets that are not included in the archive: KMT-2020-BLG-0414Lb (Zang et al., 2021a), OGLE-2019-BLG-1053Lb (Zang et al., 2021b), KMT-2019-BLG-0253Lb, KMT-2019-BLG-0953Lb, OGLE-2018-BLG-0977Lb, OGLE-2018-BLG-0506Lb, OGLE-2018-BLG-0516Lb, OGLE-2019-BLG-1492Lb (Hwang et al., 2022), KMT-2017-BLG-2509Lb, OGLE-2017-BLG-1099Lb, OGLE-2019-BLG-0299Lb (Han et al., 2021), OGLE-2016-BLG-1093Lb (Shin et al., 2022), KMT-2018-BLG-1988Lb (Han et al., 2022b), KMT-2021-BLG-0912Lb (Han et al., 2022a), OGLE-2019-BLG-0468Lb, and OGLE-2019-BLG-0468Lc (Han et al., 2022c)., 80 (59%) planets were found with the use of the data from the KMTNet survey. This can be seen in Figure 1, in which we present the histogram of microlensing planets as a function of the planet-to-host mass ratio $q$. The histogram also shows that the high-cadence surveys contribute to the detections of planets with very low mass ratios, especially those with $q<10^{-4}$.

In this paper, we report four planetary systems with low planet-to-host mass ratios detected from the microlensing surveys. Despite the short durations, ranging from a few hours to a couple of days, the planetary signals were clearly detected by the combined data of the lensing surveys. It is found that all of the discovered planets have sub-Jovian masses lying in the range of [0.05–0.38] $M_{\rm J}$, illustrating the importance of the high-cadence surveys in detecting low-mass planets.

We present the analysis of the planetary lensing events according to the following organization. In Sect. 2, we describe the observations of the individual lensing events, instrument used for observations, and the process of the data reduction. In Sect. 3, we explain the procedure of analysis that is applied to each of the individual events. In the subsequent subsections, we describe the detailed features of the planetary signals and present the results of the analyses conducted for the individual lensing events. In Sect. 4, we specify the types of the source stars and estimate the angular Einstein radii of the lens systems. In Sect. 5, we estimate the physical parameters of the planetary systems by conducting Bayesian analyses. We summarize the results of the analyses and conclude in Sect. 6.

The four lensing events for which we present analyses are (1) OGLE-2017-BLG-1691 (KMT-2017-BLG-0752), (2) KMT-2021-BLG-0320, (3) KMT-2021-BLG-1303 (MOA-2021-BLG-182), and (4) KMT-2021-BLG-1554. The source stars of all events lie toward the Galactic bulge field. In Table 1, we list the equatorial and galactic coordinates, observation fields of the surveys, alert dates, and baseline magnitudes of the individual events. The baseline magnitude $I_{\rm base}$ is approximately scaled to the OGLE-III photometry system.

The events were detected from the combined observations of the lensing surveys conducted by the KMTNet, OGLE, and MOA groups. The KMTNet survey utilizes three identical 1.6 m telescopes that are distributed in three countries of the Southern Hemisphere for the continuous coverage of lensing events. The sites of the individual telescopes are the Siding Spring Observatory in Australia (KMTA), the Cerro Tololo InterAmerican Observatory in Chile (KMTC), and the South African Astronomical Observatory in South Africa (KMTS). Observations by the OGLE survey were conducted using the 1.3 m telescope located at Las Campanas Observatory in Chile. The MOA survey uses the 1.8 m telescope at the Mt. John Observatory in New Zealand. Observations were done mainly in the $I$ band for the KMTNet and OGLE surveys and in the customized MOA-$R$ band for the MOA survey. A subset of images were acquired in the $V$ band for the purpose of estimating source colors. The detailed procedure of the source color estimation will be discussed in Sect. 4.

Reduction and photometry of the data were done using the pipelines of the individual survey groups: Albrow et al. (2009) for the KMTNet survey, Woźniak (2000) for the OGLE survey, and Bond et al. (2001) for the MOA survey. All these pipelines apply the difference image analysis algorithm (Tomaney & Crotts, 1996; Alard & Lupton, 1998) developed for the optimal photometry of stars lying in very dense star fields. For a subset of the KMTC data set, we carried out additional photometry utilizing the pyDIA code (Albrow, 2017) for the specification of the source colors. Following the routine described in Yee et al. (2012), we rescale the error bars of data by $\sigma=k(\sigma_{\rm min}^{2}+\sigma_{0}^{2})^{1/2}$, where $\sigma_{0}$ represents the error estimated from the photometry pipeline, $\sigma_{\rm min}$ is a factor used to make the data consistent with the scatter of data, and the factor $k$ is used to make $\chi^{2}$ per degree of freedom for each data set become unity. In Table 2, we list the factors $k$ and $\sigma_{\rm min}$ of the individual data sets.

The light curves of the analyzed events share a common characteristic that short-lived anomalies appear on the otherwise smooth and symmetric form of a single-lens single-source (1L1S) event. Such anomalies in lensing light curves can be produced by two channels, in which the first channel is a perturbation induced by a low-mass companion, such as a planet, to the lens (Gould & Loeb, 1992), and the second channel is an anomaly caused by a faint companion to the source (Gaudi, 1998). Hereafter we denote events with a binary lens and a binary source as 2L1S and 1L2S events, respectively. We examine the origins of the anomalies by modeling the light curve of the individual events under these 2L1S and 1L2S interpretations.

Lensing light curves are described by the combination of various lensing parameters. For a 1L1S event, the light curve is described by three parameters of $(t_{0},u_{0},t_{\rm E})$, which denote the time of the closest approach of the source to the lens, the separation (scaled to the angular Einstein radius $\theta_{\rm E}$) between the source and lens at that time, and the time scale of the event, respectively. The event time scale is defined as the time required for a source to transit $\theta_{\rm E}$.

In addition to these basic parameters, describing the light curve of a 2L1S event requires one to include extra parameters of $(s,q,\alpha)$, which represent the separation (scaled to $\theta_{\rm E}$) and mass ratio between the binary lens components, and the angle between the binary-lens axis and the direction of the source motion (source trajectory angle), respectively. Because planet-induced anomalies are usually generated by the crossings over or close approach of the source to the planet-induced caustics, an additional parameter of the normalized source radius $\rho$, which is defined as the ratio of the angular radius of the source $\theta_{*}$ to $\theta_{\rm E}$, is needed to describe the deformation of the anomaly by finite-source effects (Bennett & Rhie, 1996). In computing finite-source magnifications, we consider the limb-darkening variation of the source.

One also needs extra parameters to describe the lensing light curve of a 1L2S event. These parameters are $(t_{0,2},u_{0,2},q_{F})$, which represent the closest approach time and separation between the lens and the second source, and the flux ratio between the binary source stars, respectively. In the 1L2S model, we designate the lensing parameters related to the primary source, $S_{1}$, as $(t_{0,1},u_{0,1})$ to distinguish them from those related to the source companion, $S_{2}$. In order to consider finite-source effects occurring when the lens passes over either of the source stars, we add two additional parameters of the normalized source radii $\rho_{1}$ and $\rho_{2}$ for the lens transits over $S_{1}$ and $S_{2}$, respectively (Dominik, 2019).

In modeling 1L1S and 1L2S light curves, for which the lensing magnification is smooth with the variation of the lensing parameters, we search for the solution of the lensing parameters via a downhill approach by minimizing $\chi^{2}$ using the Markow Chain Monte Carlo (MCMC) algorithm. In modeling 2L1S light curves, for which the lensing magnification variation is discontinuous due to the formation of caustics and there may exist multiple local solutions caused by various types of degeneracy, we model the light curves in two steps. In the first step, we conduct grid searches for the binary parameters $s$ and $q$, construct a $\chi^{2}$ map on the $s$–$q$ parameter plane, and then identify local solutions appearing on the $\chi^{2}$ map. In the second step, we polish the individual local solutions using the downhill approach. Below we present the details of the modeling conducted for the individual lensing events.

Among the four analyzed planetary events, the anomalies of the three events (KMT-2017-BLG-0752, KMT-2021-BLG-1303, and KMT-2021-BLG-1554) were affected by finite-source effects, and thus the normalized source radii can be measured. In this section, we estimate the angular Einstein radii for these events. Estimating $\theta_{\rm E}$ from a measured $\rho$ value requires one to specify the source type, from which the angular source radius $\theta_{*}$ is deduced and the Einstein radius is determined by

Although the normalized source radius and thus $\theta_{\rm E}$ cannot be measured for the event KMT-2021-BLG-0320, we specify the source type for the sake of completeness.

The specification of the source type is done by estimating the color and brightness of the source. We measure the $I$ and $V$-band magnitudes of the source from the regression of the data processed using the pyDIA photometry code (Albrow, 2017) with the variation of the lensing magnification. We then place the source on the instrumental color-magnitude diagram (CMD) of stars lying around the source constructed using the same photometry code. Following the method of Yoo et al. (2004), the instrumental source color and magnitude, $(V-I,I)$, are then calibrated using the centroid of red giant clump (RGC), for which its reddening and extinction-corrected (de-reddened) color and magnitude, $(V-I,I)_{\rm RGC,0}$, are known, on the CMD as a reference.

Figure 10 shows the positions of the source stars (marked by blue dots) with respect to those of the RGC centroids (red dots) on the CMDs of the individual events. For OGLE-2017-BLG-1691, the source color could not be securely measured not only because the $V$-band data sparsely covered the light curve during the lensing magnification but also because the photometry quality of these data is low, although the $I$-band magnitude was relatively well measured. In this case, we estimated the source color as the median color of stars with the same $I$-band magnitude offset from the RGC centroid in the CMD constructed from the images of Baade’s window taken from the observations using the Hubble Space Telescope (Holtzman et al., 1998). From the offsets in color and magnitudes between the source and RGC centroid, $\Delta(V-I,I)$, together with the known de-reddened color and magnitude of the RGC centroid, $(V-I,I)_{\rm RGC,0}$ (Bensby et al., 2013; Nataf et al., 2013), we estimate the calibrated source color and magnitude as $(V-I,I)_{0}=(V-I,I)_{\rm RGC,0}+\Delta(V-I,I)$. In Table 7, we list the source colors and magnitudes of the individual events estimated from this procedure along with the spectral types of the source stars. It is found that the source of OGLE-2017-BLG-1691 is a turnoff star or a subgiant of a G spectral type, while the source stars of the other events are main-sequence stars with spectral types ranging from G to K.

For each event, the angular source radius and Einstein radius were estimated from the measured color and magnitude of the source. For this, the measured $V-I$ color was converted into $V-K$ color using the color-color relation of Bessell & Brett (1988), $\theta_{*}$ value was interpolated from the ($V-K$)–$\theta_{*}$ relation of Kervella et al. (2004), and then the angular Einstein radius was estimated using the relation in Equation (3). With the measured Einstein radius together with the event time scale, the value of the relative lens-source proper motion was assessed as

In Table 8, we list the estimated values of $\theta_{*}$, $\theta_{\rm E}$, and $\mu$ for the individual events. The $\theta_{\rm E}$ and $\mu$ values for the event KMT-2021-BLG-0320 are left blank because finite-source effects in the lensing light curve were not detected and subsequently the values of $\rho$, $\theta_{\rm E}$, and $\mu$ could not be measured. We note that the angular Einstein radius of KMT-2021-BLG-1554, $\theta_{\rm E}\sim 0.10$ mas, is substantially smaller than those of the other events, and this together with its short time scale, $t_{\rm E}\sim 5$ days, suggests that the mass of the lens would be very low. KMT-2021-BLG-1554 is the seventh shortest microlensing event with a bound planet. See Table 3 of Ryu et al. (2021).

In this section, we estimate the physical parameters of the planetary systems. For the unique constraint of the physical lens parameters, one must simultaneously measure the extra observables of $\theta_{\rm E}$ and $\pi_{\rm E}$, from which the mass $M$ and distance to the lens, $D_{\rm L}$, are determined as

Here $\kappa=4G/(c^{2}{\rm AU})$, $\pi_{\rm S}={\rm AU}/D_{\rm S}$, and $D_{\rm S}$ denotes the distance to the source (Gould, 1992, 2000). The values of the microlens parallax could not be measured for any of the events, and thus the physical parameters cannot be unambiguously determined from the relation in Equation (5). However, one can still constrain $M$ and $D_{\rm L}$ using the other measured observables of $t_{\rm E}$ and $\theta_{\rm E}$, which are related to the physical lens parameters as

where $\pi_{\rm rel}={\rm AU}(D_{\rm L}^{-1}-D_{\rm S}^{-1})$ denotes the relative parallax between the lens and source. The event time scales were well measured for all events, and the Einstein radii were assessed for three of the four events. In order to estimate the physical lens parameters with the constraints provided by the measured observables of the individual events, we conduct Bayesian analyses using a Galactic model.

In the Bayesian analysis, we started by producing many lensing events from a Monte Carlo simulation conducted with the use of a Galactic model, which defines the matter-density and kinetic distributions, and mass function of Galactic objects. We adopted the Galactic model constructed by Jung et al. (2021). In this model, the density distributions of disk and bulge objects are described by the Robin et al. (2003) and Han & Gould (2003) models, respectively. The kinematic distribution of disk objects is based on the modified version of the Han & Gould (1995) model, in which the original version is modified to reconcile the changed density model, that is, the Robin et al. (2003) model. The bulge kinematic distribution is modeled based on proper motions of stars in the Gaia catalog (Gaia Collaboration, 2016, 2018). For the details of the density and kinematic distributions, see Jung et al. (2021). In the Galactic model, the mass function is constructed with the adoption of the initial mass function and the present-day mass function of Chabrier (2003) for the bulge and disk lens populations, respectively.

In the second step, we computed the time scales and Einstein radii of the simulated events using the relations in Equation (6), and then constructed posterior distributions of $M$ and $D_{\rm L}$ for the simulated events with the $t_{\rm E}$ and $\theta_{\rm E}$ values that are consistent with the observables of the individual lensing events. For the three events OGLE-2017-BLG-1691, KMT-2021-BLG-1303, and KMT-2021-BLG-1554, we use the constraints of both $t_{\rm E}$ and $\theta_{\rm E}$, and for KMT-2021-BLG-0320, we apply the constraint of only $t_{\rm E}$ because $\theta_{\rm E}$ is not measured for the event.

Figures 11 and 12 show the Bayesian posteriors of $M$ and $D_{\rm L}$ of the individual events, respectively. In Table 9, we summarize the estimated values of the host and planet masses, $M_{\rm host}$ and $M_{\rm planet}$, distance, and projected host-planet separation, $a_{\perp}=sD_{\rm L}\theta_{\rm E}$, for all of which medians are presented as representative values and the uncertainties are estimated as 16% and 84% of the Bayesian posterior distributions. The median values and uncertainty ranges of the individual events are marked by solid and dotted vertical lines in the Bayesian posteriors presented in Figures 11 and 12, respectively. For the events with degenerate solutions, OGLE-2017-BLG-1691, KMT-2021-BLG-0320 and KMT-2021-BLG-1554, we present the planetary separations $a_{\perp}$ corresponding to both the close and wide (or inner and outer) solutions. We note that the uncertainties of the estimated physical parameters are big because of the intrinsically weak Bayesian constraint. For example, from the comparison of the posterior distributions of OGLE-2017-BLG-1691 and KMT-2021-BLG-0320, one finds that the difference between the two posterior distributions is not significant, although the mean lens mass for the former event is slightly bigger than that of the latter event due to the longer time scale and the uncertainty is smaller due to the additional constrain of $\theta_{\rm E}$.

The estimated masses indicate that all of the discovered planets have sub-Jovian masses. The planet masses KMT-2021-BLG-0320L, KMT-2021-BLG-1303L, and KMT-2021-BLG-1554L correspond to $\sim 0.10$, $\sim 0.38$, and $\sim 0.12$ times of the mass of the Jupiter, and the planet mass of OGLE-2017-BLG-1691L corresponds to that of Uranus. To be noted among the planet hosts is that the estimated mass of the planetary system KMT-2021-BLG-1554L, $M_{\rm host}\sim 0.08\leavevmode\nobreak\ M_{\odot}$, corresponds to the boundary between a star and a brown dwarf (BD). Together with the previously detected planetary systems with very low-mass hosts⁴⁴4MOA-2011-BLG-262 (Bennett et al., 2014), OGLE-2012-BLG-0358 (Han et al., 2013), MOA-2015-BLG-337 (Miyazaki et al., 2018), OGLE-2015-BLG-1771 (Zhang et al., 2020), KMT-2016-BLG-1820 (Jung et al., 2018a), KMT-2016-BLG-2605 (Ryu et al., 2021), OGLE-2017-BLG-1522 (Jung et al., 2018b), OGLE-2018-BLG-0677 (Herrera-Martín et al., 2020), KMT-2018-BLG-0748 (Han et al., 2020b), and KMT-2019-BLG-1339L (Han et al., 2020a), the discovery of the system demonstrates the microlensing capability of detecting planetary systems with very faint or substellar hosts. Besides KMT-2021-BLG-1554L, the host stars of the other planetary systems are low-mass stars with masses lying in the range of $\sim[0.3$–$0.6]\leavevmode\nobreak\ M_{\odot}$. Under the approximation that the snow line distance scales with the host mass as $a_{\rm sl}\sim 2.7(M/M_{\odot})$ AU, all discovered planets lie beyond the snow lines of the hosts regardless of the solutions, demonstrating the high microlensing sensitivity to cold planets. The planetary systems lie in the distance range of $\sim[6.3$–$7.6]$ kpc, demonstrating the usefulness of the microlensing method in detecting remote planets.

We presented the analyses of four planetary microlensing events OGLE-2017-BLG-1691, KMT-2021-BLG-0320, KMT-2021-BLG-1303, and KMT-2021-BLG-1554. The events share a common characteristic that the planetary signals appeared as anomalies with very short durations, ranging from a few hours to a couple of days, and they were clearly detected solely by the combined data of the high-cadence lensing surveys without additional data from followup observations.

From the detailed analyses of the events, it was found that the signals were generated by planets with low planet-to-host mass ratios: three of the planetary systems with mass ratios of the order of $10^{-4}$ and the other with a mass ratio slightly greater than $10^{-3}$. In the histogram of microlensing planets presented in Figure 1, we mark the positions of the four planets discovered in this work. The estimated masses indicated that all discovered planets have sub-Jovian masses, in which the planet masses of KMT-2021-BLG-0320Lb, KMT-2021-BLG-1303Lb, and KMT-2021-BLG-1554Lb correspond to $\sim 0.10$, $\sim 0.38$, and $\sim 0.12$ times of the mass of the Jupiter, and the mass of OGLE-2017-BLG-1691Lb corresponds to that of the Uranus. It was found that the host of the planetary system KMT-2021-BLG-1554L has a mass at around the boundary between a star and a brown dwarf. Besides this system, it was found that the host stars of the other planetary systems are low-mass stars with masses in the range of $\sim[0.3$–$0.6]\leavevmode\nobreak\ M_{\odot}$. The discoveries of the planets well demonstrate the capability of the current high-cadence microlensing surveys in detecting low-mass planets.